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'''Sequentially Spent Score''' ('''SSS'''), also known as Sequentially Subtracted Score or Unitary Cardinal Voting, is a sequential [[Multi-Member System | Multi-Winner]] [[Cardinal voting systems | Cardinal voting system]] built on [[Score voting]] ballots. Each round's winner is thatthe candidate who has the highest sum of score. Between each election roundsround the ballots are adjusted such that a candidate cannot influence subsequent rounds more than the score they have remaining. This property of spending score is a particular implementation of [[Vote Unitarity]]. [[Sequentially Spent Score]] was invented by [[Keith Edmonds]] and [[Vote Unitarity]] was defined to describe this underlying theory.
 
==Procedure==
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Each voter starts with a ballot weight equal to the MAX possible score.
# Elect the candidate who is the [[Utilitarian winner]] (ie the candidate with the highest sum of score)
# Weaken the weight of the ballots that had supported that candidate in proportion to how strongly they supported that candidate, and(with surplus handling; see below)
# AdjustFor ballots that lost weight in the previous step, adjust the amount of support eachthey ballot givesgive to the remaining candidates by '''capping''' it at the reduced scoreballot weight
# Repeat these steps until all the necessary seats are filled.
 
===Surplus Handling===
 
For the second step, if that candidate had received more than a surpluspredefined threshold of supportpoints (usually defined as a Hare or Droop Quota of the ballots multiplied by the maximum score), then the amount of weight to take away from the ballots supporting thethat round's winner is to be reduced proportionally to ensure that only the equivalent in ballot weight of that certainpredefined amountthreshold of supportpoints is removed from all ballots supporting the winner. This is known as [[Factional Surplus Handling]].
 
===Variants===
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==== Scaling ====
A variant of this method can be made by scaling instead of capping to adjust ballot support for candidates after the ballot's weight has been adjusted. Capping is when, if a ballot's weight has been reduced by a certain amount, a ballot that gives a candidate more support than its weight allows is edited to give that candidate only as much support as its ballot weight. In other words, if a ballot is at 70% weight (70% power), yet it gives a candidate 80% support (a score of 8 out of 10, for example), it is adjusted to give that candidate 70% support instead.
 
 
Scaling is when the amount of support a ballot gives a candidate is proportionally adjusted by how much weight it has remaining. In other words, a ballot with 50% weight that originally gave a candidate 70% support when it had full weight will now give that candidate 35% support.
 
==== Quota of Ballot Selection ====
 
In the first step one need not choose the [[Utilitarian winner]]. A reasonable alternative is theto take the winner as the candidate who has the highest sum of score in the top Hare (or Droop ) quota of Ballots that most support them.
 
== Related Systems ==
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